Linear Algebra B 2

Course guarantor:

Lubomíra Dvořáková

Lecturer:

Dana Majerová

Tutor:

Dana Majerová

Supervisor:

Department of Software Engineering

Synopsis:

Determinant. Regular matrix, regular operator. Inverse matrix and operator. Inner product, orthogonality, Gramm-Schmidt orthogonalization process. Linear geometry. Eigenvalues, eigenvectors, diagonalization of matrices. Special types of matrices.

Requirements:

Credit is awarded after successfully writing 3 credit tests (each with at least 50% points). The exam is written (calculation of eigenvalues/vectors of a matrix, diagonalizability) and oral (the student draws 2 questions from the theory). If any part of the exam is graded F, then the total grade is F. Otherwise, the arithmetic average is calculated.

Syllabus of lectures:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Syllabus of tutorials:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Study Objective:

Knowledge of basic terms of linear algebra.

Ability to prove mathematical theorems and solve problems of linear algebra, especially work with matrices.

Study materials:

Key references:

[1] Dontová, E. Matematika III. Praha: ČVUT, 1999.

[2] Čížková, L. Sbírka příkladů z matematiky I. Praha: ČVUT, 1999.

[3] Study materials and tasks in the MOODLE system.

Recommended references:

[4] Pytlíček, J. Cvičení z algebry a geometrie. Praha: ČVUT, 1997.

Note:

Further information:

https://moodle-vyuka.cvut.cz/

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Applications of Informatics in Natural Sciences (compulsory course in the program)